If I use a periodic schedule or a certain time as a Trigger, do I also have to set it as a condition in my actions? See below rule.....Do I need to put the Time and Date into the Actions again?
Why do you have the trigger on sunday and saturday? Just make the trigger a weekday and you don't need any condition at all about time in the rule.
I saw that after I posted it. I changed it to just M-F.
You don't ever need to put condicionals in your actions. Conditionals are always optional; they just let you control the flow of execution in your actions if needed. (A common example is a trigger of contact sensor changed when you want to do something different whenever it's opened versus closed.)
In your example above, if that's a real rule, you do need the conditionals so the right set of actions runs at the appropriate time. That being said, you could also just make them into separate rules (they don't depend on each other in any way; my contact sensor example likely does since you would often a have a delay in one set of actions and a cancel for that delay in the other half, and these would need to be part of the same rule) with separate triggers. Your rule actions run only when your trigger fires (unless you call the rule from another rule), so you wouldn't need a conditional then. That being said, the way you have it now is equivalent and would also work.